Dynamics of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:mi>B</mml:mi><mml:mo>→</mml:mo><mml:mi>C</mml:mi></mml:math>Reaction Fronts in the Presence of Buoyancy-Driven Convection

Rongy, Laurence; Trevelyan, P. M. J.; Wit, A. De

doi:10.1103/physrevlett.101.084503

“…Indeed, as the volume occupied by the H 2 O molecule is larger than the sum of the volume of both H + and OH À , which can be checked by verifying that R C < R A + R B in Table 2, the reaction H + + OH À f H 2 O induces a local decrease of the solution density. 31 If this second effect is more important than the first one, the reaction zone becomes less dense than its surroundings which can induce locally RT buoyant plumes rising upward in the upper solution where the denser reactant acid solution overlies the less dense reaction zone, as illustrated in Figure 1 (top). The criterion for onset of this solutal instability depends therefore on the relative density of the acid solution versus that of the product one.…”

Section: ' Interpretation Of Experimental Resultsmentioning

confidence: 99%

Convective Mixing Induced by Acid–Base Reactions

Almarcha

¹

,

R'Honi

²

,

Decker

³

et al. 2011

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' INTRODUCTIONIn reactive systems, forced convection is an efficient way to mix reactants and hence increase the reaction rate. This is of particular importance in chemical engineering processes. Conversely, one can address the question: how can chemical reactions influence natural convection or even be at the very source of hydrodynamic motion? These issues are at the heart of numerous applications in combustion, 1,2 polymer processing, 3,4 extraction techniques, 5,6 microfluidic devices, 7À9 bioconvection, 10 traveling fronts, 11À13 and CO 2 sequestration, 14,15 to name a few.To answer such questions, experimental studies have for instance investigated chemically driven convective mixing and enhanced extraction from one phase to another, induced by reactions between reactants initially contained separately in immiscible solvents. 5,16À18 In that case, it has been shown that the flow around the interface and within the bulk solutions result from (i) the coupling between transfer of chemical species at the interface, (ii) changes by the reaction of the density of the solutions which can trigger buoyancy-driven convective motions, and (iii) reaction-induced Marangoni effects, that is, fluid motion generated by surface tension changes at the immiscible interface. The situation is therefore quite complex, and even if theoretical studies 19À21 provide some help in understanding the influence of the various parameters, there is a need to gain insight also into simpler situations where some of the various effects are isolated. In this regard, the use of miscible solvents removes the influence of both transfer rate and Marangoni effects and allows one to separately analyze the influence of purely buoyancy-driven convection.For such miscible solvents, it has been shown experimentally that putting in contact aqueous solutions of an acid and of a base in the gravity field allows one to observe a wealth of beautiful convective patterns and instabilities. 22À25 More specifically, ascending plumes can develop above the reaction front when a solution of hydrochloric acid is put on top of a denser miscible equimolar aqueous solution of sodium hydroxide. 23 The patterns are different in presence of a color indicator, 22 indicating that this species is not neutral to the convective dynamics. 24 In this context, it is of interest to analyze such miscible systems in which a simple acidÀbase reaction takes place to understand the various possible buoyancy-driven instabilities induced by the presence, in aqueous solutions, of the neutralization reaction H + + OH À f H 2 O. To do so, we study experimentally chemically driven convective motions arising when putting in contact an aqueous solution of a strong acid on top of a denser aqueous solution of a strong base in the gravity field. We explain the influence on the dynamics of changing the type of reactants used and their concentrations. In a first part, we vary the type of counterion in the basic solution at fixed concentrations. We next vary the ratio in concentrations between th...

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“…The criterion for onset of this solutal instability depends therefore on the relative density of the acid solution versus that of the product one. In the very specific case δ B = δ C = 1 of contact between reactants with equal initial concentration [a] o = [b] o , the concentration of the product in the reaction zone is half of it, 31 that is, [c] = [a] o /2. As a consequence, eq 4 shows that, if the pure acid solution has a dimensionless density F = 1, the pure base has a density F = R B , while the density at the contact point is equal to R C /2.…”

Section: ' Interpretation Of Experimental Resultsmentioning

confidence: 99%

Active Role of a Color Indicator in Buoyancy-Driven Instabilities of Chemical Fronts

Almarcha

¹

,

Trevelyan

²

,

Riolfo

³

et al. 2010

J. Phys. Chem. Lett.

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' INTRODUCTIONIn reactive systems, forced convection is an efficient way to mix reactants and hence increase the reaction rate. This is of particular importance in chemical engineering processes. Conversely, one can address the question: how can chemical reactions influence natural convection or even be at the very source of hydrodynamic motion? These issues are at the heart of numerous applications in combustion, 1,2 polymer processing, 3,4 extraction techniques, 5,6 microfluidic devices, 7À9 bioconvection, 10 traveling fronts, 11À13 and CO 2 sequestration, 14,15 to name a few.To answer such questions, experimental studies have for instance investigated chemically driven convective mixing and enhanced extraction from one phase to another, induced by reactions between reactants initially contained separately in immiscible solvents. 5,16À18 In that case, it has been shown that the flow around the interface and within the bulk solutions result from (i) the coupling between transfer of chemical species at the interface, (ii) changes by the reaction of the density of the solutions which can trigger buoyancy-driven convective motions, and (iii) reaction-induced Marangoni effects, that is, fluid motion generated by surface tension changes at the immiscible interface. The situation is therefore quite complex, and even if theoretical studies 19À21 provide some help in understanding the influence of the various parameters, there is a need to gain insight also into simpler situations where some of the various effects are isolated. In this regard, the use of miscible solvents removes the influence of both transfer rate and Marangoni effects and allows one to separately analyze the influence of purely buoyancy-driven convection.For such miscible solvents, it has been shown experimentally that putting in contact aqueous solutions of an acid and of a base in the gravity field allows one to observe a wealth of beautiful convective patterns and instabilities. 22À25 More specifically, ascending plumes can develop above the reaction front when a solution of hydrochloric acid is put on top of a denser miscible equimolar aqueous solution of sodium hydroxide. 23 The patterns are different in presence of a color indicator, 22 indicating that this species is not neutral to the convective dynamics. 24 In this context, it is of interest to analyze such miscible systems in which a simple acidÀbase reaction takes place to understand the various possible buoyancy-driven instabilities induced by the presence, in aqueous solutions, of the neutralization reaction H + + OH À f H 2 O. To do so, we study experimentally chemically driven convective motions arising when putting in contact an aqueous solution of a strong acid on top of a denser aqueous solution of a strong base in the gravity field. We explain the influence on the dynamics of changing the type of reactants used and their concentrations. In a first part, we vary the type of counterion in the basic solution at fixed concentrations. We next vary the ratio in concentrations between th...

show abstract

“…As it is the horizontal density gradients that initially induce convection one is therefore able to predict the RDC dynamics of the system on the sole basis of the Rayleigh numbers and of the RD concentration profiles. The different behaviors of the RDC system can be analytically classified as functions of R a;b;c without resorting to numerics and further when b ¼ 1 then the direction of front propagation can be found analytically as shown by Rongy et al (2008). Hence, before examining the RDC system the simple RD system is first analyzed.…”

Section: Reaction-diffusion Density Profilesmentioning

confidence: 99%

“…In this context, it is the objective of this article to extend the study of Rongy et al (2008) to the case where the reactants have different initial concentrations corresponding to an underlying moving RD front. In that case, the presence of convection also results in a deformation of the front which can furthermore be accelerated with regard to the RD situation.…”

Section: Introductionmentioning

confidence: 99%

“…In this framework, Rongy et al (2008) recently studied the influence of convection in the case where the reactants A and B have equal diffusion coefficients and equal initial concentrations for which the RD analysis predicts a non-moving front. The presence of convection cannot only deform the initially vertical planar front but can also lead to its propagation.…”

Section: Introductionmentioning

confidence: 99%

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Influence of buoyancy-driven convection on the dynamics of A+B→C reaction fronts in horizontal solution layers

Rongy

¹

,

Trevelyan

²

,

Wit

³

2010

Chemical Engineering Science

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a b s t r a c tThe dynamics of initially vertical A þ B-C reaction fronts propagating in covered horizontal solution layers can be influenced by buoyancy-driven convection. Experiments have provided evidence that a much faster propagation of the front occurs in solutions than that predicted by reaction-diffusion (RD) theories, thereby suggesting the influence of convective effects arising if A, B, and C have different densities. Here we analyze numerically and theoretically the dynamics resulting from the coupling of a simple A þ B-C chemical reaction with diffusion and convection induced by density differences across the reaction front. The important parameters of the related reaction-diffusion-convection (RDC) model are the three dimensionless Rayleigh numbers, quantifying the contribution of each species concentration to the density of the solution, the layer thickness, and the initial reactant concentration ratio. The presence of buoyancy-driven convection at the front induces a propagation of this front even in the case of equal diffusion coefficients and equal initial reactant concentrations for which RD theories predict a non-moving front. In the case of equal initial concentrations, even in the presence of convection, the classification of the various possible dynamics and the prediction of the direction of front propagation can be obtained from simple criteria on the Rayleigh numbers. In the case of different initial reactant concentrations for which, in the absence of convection, the RD front propagates towards the side of the less concentrated reactant, the introduction of buoyancy convection not only invalidates the long time RD scalings but can lead to a double reversal in the direction of propagation of the reaction front for intermediate times. The influence of the different parameters on the RDC dynamics is presented.

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Dynamics ofA+B→CReaction Fronts in the Presence of Buoyancy-Driven Convection

Cited by 65 publications

References 11 publications

Convective Mixing Induced by Acid–Base Reactions

Convective Mixing Induced by Acid–Base Reactions

Active Role of a Color Indicator in Buoyancy-Driven Instabilities of Chemical Fronts

Influence of buoyancy-driven convection on the dynamics of A+B→C reaction fronts in horizontal solution layers

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